An evaluation of lower bound limit pressures for thick and moderately thick vessels having ellipsoidal inside surfaces

Lower bound limit pressures are evaluated for thick and moderately thick vessels of constant thickness having ellipsoidal inside surfaces. A three-dimensional stress formulation is written in terms of the stresses. The stresses are expressed in terms of an independent set of variables. Using a non-linear programming method the stress variables are optimized to give a maximum limit pressure for a von Mises yield criterion. Computed results are presented for a range of semi-major axis to thickness and major-to-minor axis ratios.     

An exact solution for stresses and displacements of pressurized FGM thick-walled spherical shells with exponential-varying properties

Exact closed-form solutions have been derived for stresses and the displacements in thick spherical shells made of functionally graded materials with exponential-varying properties subjected to internal and external pressure. Poisson’s ratio is assumed to be constant. The obtained results show that the inhomogeneity properties of FGMs have a significant influence on the displacement and stresses distribution along the radial direction. A numerical solution using finite element method is also presented and good agreement was found between the analytical solutions and the solutions carried out through the FEM. The values used in this study are arbitrarily chosen to demonstrate the effect of inhomogeneity on displacements and stresses distributions.     

Lower bound to limit pressure for cylindrical shell with part-through slot

A lower bound to the limit pressure of a cylindrical shell with a rectangular slot part through the thickness at mid-length is computed using a linear optimization technique. The sides of the slot are axial and circumferential.The analysis has been carried out for internal pressure applied to the cylinder such that the longitudinal pressure end force is (a) not taken by the cylindrical shell, (b) wholly taken by the cylindrical shell.Different proportions of rectangular slot and different radius to thickness ratios of the cylinder have been considered. Results are presented for a range of parameters.     

内压圆筒厚度计算公式分析讨论

GB 150—2011中采用的是弹性失效准则,规定对设计压力p≤0.4[σ]t的内压圆筒厚度按中径公式进行设计。JB 4732—1995中规定对设计压力p≤0.4[σ]t的内压圆筒厚度按中径公式进行设计,设计压力p>0.4[σ]t时按Tresca全屈服压力进行设计。比较研究表明:基于弹性失效准则时,中径公式算出的厚度最薄;基于塑性失效准则时,中径公式算出的厚度最厚;当径比较小时,按Tresca全屈服压力和中径公式算出的内压圆筒厚度相差很小,在工程设计中,可以统一采用Tresca全屈服压力计算内压圆筒壁厚。     

Influence of inclusion pairs, clusters and stringers on the lower bound of the endurance limit of bearing steels

The lower bound of the endurance limit, defined as the maximal Hertzian pressure that does not induce any micro-plastic strain around inclusions, is computed for groups of inclusions in a bearing steel subjected to contact stresses. An extension of the Eshelby analytical method is used for determining local stresses around inclusions. Configurations such as pairs, stringers or clusters of identical spherical inclusions of alumina in a 100Cr6 matrix are analysed. In the Hertzian stress field, the interaction is revealed to be anisotropic, with a large decrease of the endurance limit for stringer axes close to the normal to contact surface.     

Limit pressures for cylindrical shells with two adjacent circular cut outs

Cylindrical shells each with two equal circular openings were subjected to internal pressure until gross plastic deformation occurred. The opening diameter was kept constant throughout but the pitch was varied and two vessel sizes were used. In some specimens the two openings were disposed around the shell circumferentially and in some they were disposed along a cylinder generator. The experimental limit pressures so determined were compared with those calculated by using a lower bound analysis. Experimental limit pressures were also compared with those determined from tests on three specimens each having two adjacent openings with branch reinforcement.     

Vibration and stability of angle-ply laminated composite plates subjected to in-plane stresses

Natural frequencies and buckling stresses of angle-ply laminated composite plates are analyzed by taking into account the effects of shear deformation, thickness change and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for thick rectangular laminates subjected to in-plane stresses is derived through Hamilton's principle. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported thick laminated plate. In order to assure the accuracy of the present theory, convergence properties of the fundamental natural frequency are examined in detail. Numerical results are compared with those of the published existing theories. The modal displacement and stress distributions in the thickness direction are obtained and plotted in figures. The present global higher-order approximate theories can predict the natural frequencies, buckling stresses and modal stresses of thick multilayered angle-ply composite laminates accurately within small number of unknowns which is not dependent on the number of layers.     

Maximum load for toruslike shells

Maximum loads for toruslike shells with constant thickness loaded with an axial force, internal pressure, and a bending torque are calculated. The rigid plastic body model, the Tresca yield condition, and the plastic yield law associated with it are used. Application of the finite element method for calculation of the maximum load on a shell is considered. A significant increase in the characteristic deformation of a shell is used as a criterion. The corresponding formulas for maximum loads are obtained based on the kinematic method of the limit equilibrium theory. The difference between the obtained results and the static solution does not exceed 3%.     

Vibration and buckling of cross-ply laminated composite circular cylindrical shells according to a global higher-order theory

Natural frequencies and buckling stresses of cross-ply laminated composite circular cylindrical shells are analyzed by taking into account the effects of higher-order deformations such as transverse shear and normal deformations, and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for laminated composite circular cylindrical shells made of elastic and orthotropic materials is derived through Hamilton's principle. Several sets of truncated approximate higher-order theories are applied to solve the vibration and buckling problems of laminated composite circular cylindrical shells subjected to axial stresses. The total number of unknowns does not depend on the number of layers in any multilayered shells. In order to assure the accuracy of the present theory, convergence properties of the first natural frequency and corresponding buckling stress for the fundamental mode r=s=1 are examined in detail. The internal and external works are calculated and compared to prove the numerical accuracy of solutions. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. It is noticed that the present global higher-order approximate theories can predict accurately the natural frequencies and buckling stresses of simply supported laminated composite circular cylindrical shells within small number of unknowns.     

功能梯度压电材料壳体热残余应力

功能梯度压电材料结构成型冷却后会出现热残余现象,影响结构强度.借鉴复合材料层合结构的研究方法,将功能梯度压电材料球壳和圆柱壳沿厚度分为若干层,各层视为均匀材料,根据层间连续条件导出递推关系,得到显式的力—电—热多场耦合热残余解.统一了多层功能梯度压电材料壳体和连续功能梯度压电材料壳体热残余解.对于前者,其解为精确解;对于后者,其解为渐近解,随层数增加而收敛于精确解.其解也适用于功能梯度压电材料涂层.该方法对材料性能的变化方式(函数)没有要求,适应性强.并讨论影响热残余应力和界面强度的因素,球壳因双曲率的影响,热残余应力显著大于柱壳.     

A three-dimensional finite element method for plate bending

A three-dimensional finite element method is proposed for plate bending. The displacement function is assumed to have a particular form with respect to the thickness variable.The assumed displacement function is substituted into the three-dimensional potential energy functional and a two-dimensional variational problem emerges.The two-dimensional problem is treated by the finite element method and it is seen that for conforming solutions the only requirement is continuity of the basis functions.The method includes transverse shear and thickness effects and may be used for both thin and moderately thick shells.To illustrate the method and to compare it with other results, the problems of a square plate under point and distributed loads and with simply supported and clamped boundary are treated numerically.     

Effect of hard and stiff overlay coatings on the strength of surfaces in repeated sliding

Most work on the strength of coated surfaces has assumed that there are no residual stresses and that the load is applied only once. Both these assumptions are incorrect. The manufacturing process itself may develop large residual stresses in the surface and repeated sliding causes the load to be applied many times, leading to the development of residual stresses. These residual stresses are protective in nature so that a load which causes yielding in the first pass may be supported purely elastically in the steady state. The load limit for elastic steady state is known as the shakedown limit and is the rational design criterion in bearing industries. In the present paper, the effect of coating thickness, coating stiffness and the friction coefficient on the shakedown limit has been investigated and the results are presented in the form of non-dimensional maps.     

Thermomechanical postbuckling analysis of moderately thick functionally graded plates and shallow shells

In this paper, an analytical solution is provided for the postbuckling behaviour of moderately thick plates and shallow shells made of functionally graded materials (FGMs) under edge compressive loads and a temperature field. The material properties of the functionally graded shells are assumed to vary continuously through the thickness of the shell, according to a power law distribution of the volume fraction of the constituents. The fundamental equations for moderately thick rectangular shallow shells of FGM are obtained using the von Karman theory for large transverse deflection and high-order shear deformation theory for moderately thick plates. The solution is obtained in terms of mixed Fourier series and the obtained results are compared with those of the Reissner–Mindlin's theory for moderately thick plates and the classical theory ignoring transverse shear deformation. The effect of material properties, boundary conditions and thermomechanical loading on the buckling behaviour and the associated stress field are determined and discussed. The results reveal that thermomechanical coupling effects and the boundary conditions play a major role in dictating the response of the functionally graded plates and shells under the action of edge compressive loads.     

Stochastic hybrid numerical method for transient analysis of stress field in functionally graded thick hollow cylinders subjected to shock loading

This investigation aims to study the random stresses in a functionally graded (FG) thick hollow cylinder with uncertain material properties subjected to mechanical shock loading using a hybrid numerical method. The mechanical properties are considered to vary across thickness of FG cylinder as a nonlinear power function of radius. The stresses are obtained by solving Navier equation and using Galerkin finite element and Newmark finite difference methods. The Monte Carlo simulation is used to generate the random mechanical properties for the problem. The failure probabilities and time history analysis of stresses are determined for various coefficient of variation considering various grading patterns of mechanical properties. The presented hybrid numerical method is effective, with high capability for stochastic analysis of dynamic and transient analysis of FG structures with various boundary conditions.     

弹性圆柱壳的稳定性优化设计

研究任意轴对称边界条件下和受均布法向载荷作用圆柱壳的稳定性优化设计问题，即极大化屈曲临界载荷。利用能量原理分析轴对称变厚度圆柱壳的分支点屈曲，将求解屈曲临界载荷变成求解广义特征值方程，使圆柱壳稳定性优化设计成为极大化最小特征值问题。实际算例验证了本方法的有效性。研究结果可用于圆柱壳的加肋优化设计。     

Effect of methods for fixing and loading of cylindrical shells on their stability and supercritical behavior

The effect of the methods of fixing and external-pressure loading of an elastic isotropic cylindrical shell on its sub- and supercritical deformation is investigated. A geometrically nonlinear statement of the edge problem in the form of the technical theory of finite deflection hollow shells is applied. The edge problem is digitized with the Rayleigh-Ritz method. The solution to the set of nonlinear algebraic equations is sought using the methods of continuation by the parameter close to the optimal one. The versions of shell sealing and supporting as well as uniform lateral pressure and uniform compression are considered. The trajectories of shell loading are plotted and the shapes of their supercritical equilibrium states are found. The axial compressing load is found to exert a larger effect on the upper and lower critical pressure as compared to the conditions of shell end fixing. Moreover, axial loading of short shells yields an increase in the critical pressure rather than its decrease, as is customary in the theory of shell stability.     

Strip Layer Method for Analysis of the Three-Dimensional Stresses and Spread of Large Cylindrical Shell Rolling

As the traditional forging process has many problems such as low efficiency, high consumption of material and energy, large cylindrical shell rolling is introduced. Large cylindrical shell rolling is a...     

热-机荷载作用的P-FGM扁球壳跳跃屈曲分析

基于经典壳体理论和Sanders非线性应变-位移关系,导出了幂律型功能梯度材料(P-FGM)扁球壳在热-机械荷载作用下的几何非线性常微分控制方程。推导过程考虑了沿厚度存在一维热传导温度场和法向均布荷载作用。采用打靶法求解了由控制方程和固定夹紧边界条件构成的两点边值问题。得到了FGM扁球壳的一些典型的屈曲平衡路径和双稳态构形。对热-机械荷载作用的FGM扁球壳的跳跃屈曲行为进行了参数影响分析。结果表明：温度上升时,球壳上临界荷载显著增加、下临界荷载变化不明显。梯度指数增加时,球壳上、下临界荷载均显著减小。组分材料模量增加时,球壳上、下临界荷载均显著增加。当底圆半径和厚度给定时,随壳体中面曲率半径增加,球壳上、下临界荷载均显著增加。当中面曲率半径和厚度给定时,随底圆半径增加,球壳下临界荷载显著减小,上临界荷载几乎不变。     

Limit loads for cylindrical shells subjected to local longitudinal bending moments

Tests have been carried out on mild steel cylindrical shells, each with a radial square bar attachment welded at its mid length. Loads were applied to each attachment so that the shell was subjected to a longitudinal bending moment. On four specimens, elastic strains were measured so that stress distributions in the shell could be compared with theoretical distributions. Fourteen specimens were loaded so that gross deformation took place. Deformations and strains were measured and on two specimens, crack patterns on an oxide layer were observed. With increasing load, the plastic deformation of specimens developed gradually and not in the sudden manner associated with theoretical rigid-plastic collapse. Experimental plastic limit moments are compared with theoretical values calculated by an upper bound analysis. The range of radius/thickness values investigated was 18·3–53·5, and the half width/radius ratios were between 0·120 and 0·356.     

Necessary conditions for the instability of spherical shells under external pressure

Results are presented of investigations into determining the limit of the magnitudes of uniform external pressure, which when exceeded may cause the possible stability loss of equilibrium states of geometrically perfect ideally elastic spherical shells. Results of calculations of pressures corresponding to this boundary and understanding the necessary conditions of instability of the shells under consideration are close qualitatively and quantitatively to the lower boundary of their experimentally determined critical values. Investigations are performed based on the dynamic criterion of stability and equations of the unperturbed motion of shells linearized in the vicinity of the equilibrium states under consideration.